Circadian Rhythms in Rho1 Activity Regulate Neuronal Plasticity and Network Hierarchy

Neuronal plasticity helps animals learn from their environment. However, it is challenging to link specific changes in defined neurons to altered behavior. Here, we focus on circadian rhythms in the structure of the principal s-LNv clock neurons in Drosophila. By quantifying neuronal architecture, we observed that s-LNv structural plasticity changes the amount of axonal material in addition to cycles of fasciculation and defasciculation. We found that this is controlled by rhythmic Rho1 activity that retracts s-LNv axonal termini by increasing myosin phosphorylation and simultaneously changes the balance of pre-synaptic and dendritic markers. This plasticity is required to change clock network hierarchy and allow seasonal adaptation. Rhythms in Rho1 activity are controlled by clock-regulated transcription of Puratrophin-1-like (Pura), a Rho1 GEF. Since spinocerebellar ataxia is associated with mutations in human Puratrophin-1, our data support the idea that defective actin-related plasticity underlies this ataxia.Courant Institute of Mathematical Sciences (Postdoctoral Fellowship

Gravitational Lorentz Violations from M-Theory

In an attempt to bridge the gap between M-theory and braneworld phenomenology, we present various gravitational Lorentz-violating braneworlds which arise from p-brane systems. Lorentz invariance is still preserved locally on the braneworld. For certain p-brane intersections, the massless graviton is quasi-localized. This also results from an M5-brane in a C-field. In the case of a p-brane perturbed from extremality, the quasi-localized graviton is massive. For a braneworld arising from global AdS_5, gravitons travel faster when further in the bulk, thereby apparently traversing distances faster than light.Comment: 13 pages, 1 figure, LaTeX, references added, minor corrections and addition

On a relation between Liouville field theory and a two component scalar field theory passing through the random walk

In this work it is proposed a transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the quantum Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field.Comment: 15 pages, 4 figures, LaTeX + RevTeX 4. With respect to the previous version an appendix has been added to provide an alternative proof of Eq. (31). Title and abstract have been change

Zeta functions, renormalization group equations, and the effective action

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories.Comment: 4 pages, ReV-TeX 3.

Chiral anomaly for local boundary conditions

It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this paper we apply the heat kernel methods to calculate boundary contributions to the chiral anomaly for local (bag) boundary conditions. As a by-product some new results on the heat trace asymptotics are also obtained.Comment: 20 p., late

Plane waves with weak singularities

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which do not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity.Comment: 22 pages, Added references and clarifying comment

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.